As an eight-week election campaign stretches out ahead of us like a trackless desert, it might be useful to take a bearing on where the prime minister stands in relation to the conservative side of the media, elements of which play themselves into the election game as self-anointed kingmakers.

One such kingmaker is Sydney-based commercial radio talkback host Alan Jones.

Malcolm Turnbull has refused to appear on the Jones program for the past two years. This might reflect a strategy to differentiate himself from Tony Abbott, who was a Jones favourite, as well as a show of genuine contempt for Jones’ sense of self-importance.

The current tension dates back to the febrile political aftermath of the now-notorious Abbott-Hockey budget of 2014. Turnbull was communications minister, and it was in that capacity that he appeared on the Jones program.

It didn’t start well:

Jones: Can I begin by asking you if you could say after me this? “As a senior member of the Abbott government I want to say here I am totally supportive of the Abbott-Hockey strategy for budget repair”.

Turnbull: Alan I am not going to take dictation from you.

And sometime later Jones says to Turnbull:

You have no hope ever of being the leader. You’ve got to get that into your head. No hope ever.

Not the happiest of prognostications.

But time passes, elections loom, and mutual interests assert themselves. In the symbiosis between politicians and the media, Turnbull needs to reach Jones’ audiences, particularly in Western Sydney and in Queensland, and Jones needs the kudos that comes with having the prime minister on his program.

And so there is talk of rapprochement.

Not that Jones is demonstrating anything like a diminution in his sense of superbia. He is quoted as saying:

No-one has ever won an election by not appearing on my program.

A clever form of words.

It just means that every candidate for prime minister – win or lose – has appeared on his program.

It does not mean that those who won did so because they appeared on his program, though that’s clearly what Jones wants people to believe.

Jones is syndicated across more than 70 stations, mainly in NSW and Queenland, but to think that he can make and unmake prime ministers is absurd. His 2GB Sydney audience on May 6, 2016, for his interview with Opposition Leader Bill Shorten was 167,000. His audience share in that city has been in steady decline for the past five years, from about 20% in 2010 to about 14% in 2015.

After being syndicated to 4BC in Brisbane in June 2015, his audience share there declined 1.2 points to 5.2% of the breakfast audience over the first two ratings periods.

So let us say on a generous estimate his total audience is 300,000, not all of whom are of voting age.

There are nearly 15 million voters in Australia, so Jones’ audience probably amounts to less than 2% of the voting population.

An analysis by Clive Hamilton in 2006 showed that Jones’ audience was far more likely to vote conservative than was the electorate as a whole: 65% of Jones listeners compared with, typically, between 48% and 52% at elections. So, to a large extent, he preaches to the converted.

His listeners were also disproportionately older – 68% over 50 compared with 37% in the over-14 population as a whole, and with a tendency to be on low-to-middle incomes. Although Hamilton’s analysis is ten years old, audience characteristics like this don’t change much.

So Jones might make a marginal difference in a few marginal seats, but kingmaker? No.

As for Turnbull’s relationship with Rupert Murdoch’s News Corp newspapers, another element in the conservative media with kingmaking aspirations, there are signs of it being not quite settled.

The Australian’s reception of the budget was no more than measured, and the Herald Sun’s was positively contemptuous. Its front-page headline was “A pop-gun budget”, with Turnbull and Treasurer Scott Morrison depicted as a couple of hapless tommies like characters from Dad’s Army.

The Daily Telegraph, however, fell over itself in admiration, depicting Morrison as Superman and acclaiming him as the “hero of the hard worker”. With its heroic blue-sky backdrop, it was reminiscent of a 1970s propaganda poster from somewhere behind the Iron Curtain.

Rupert has always been careful about overtly claiming kingmaker status. When the egregious Kelvin MacKenzie, as editor of the London Sun, claimed “It’s The Sun Wot Won It” after the British Conservative Party’s win in 1992, Rupert was reported to have rejoiced privately but when confronted publicly with statements that it showed how influential he was, he deprecated the headline as unwontedly boastful.

Yet it suits Rupert that the perception of decisive influence persists.

However hard it might be to measure that influence, the fact is that in Australia he has a newspaper monopoly in Brisbane, Adelaide and Hobart, as well as the mass-circulation Herald Sun in Melbourne and Daily Telegraph in Sydney. The latter plays to much the same audience as Jones.

With these two elements of the conservative media, then, Turnbull has some work to do. And that’s before we even think what the combined forces of Peta Credlin and Mark Latham on Sky television might unleash.